%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU967^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:53:36 AM UTC 2026 % Result : Theorem 0.47s 0.66s % Output : Proof 0.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU967^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n016.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 18:03:54 EDT 2026 % 0.18/0.35 % CPUTime : % 0.29/0.50 %----Proving TH0 % 0.47/0.66 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.47/0.66 % SZS status Theorem % 0.47/0.66 % SZS output start Proof % 0.47/0.66 ( % 0.47/0.66 (declare-sort $$unsorted 0) % 0.47/0.66 (declare-const tptp.cH_0 (-> (-> (-> $$unsorted $$unsorted) Bool) $$unsorted $$unsorted)) % 0.47/0.66 (declare-const tptp.cP_0 (-> $$unsorted Bool)) % 0.47/0.66 (declare-const tptp.cG_0 (-> (-> (-> $$unsorted $$unsorted) Bool) $$unsorted $$unsorted)) % 0.47/0.66 (declare-const tptp.cY_0 (-> (-> (-> $$unsorted $$unsorted) Bool) $$unsorted)) % 0.47/0.66 (define @t1 () (@var "Xw_2" $$unsorted)) % 0.47/0.66 (define @t2 () (@var "Xw_1144" (-> $$unsorted $$unsorted))) % 0.47/0.66 (define @t3 () (@var "Xm_5" (-> (-> $$unsorted $$unsorted) $$unsorted Bool))) % 0.47/0.66 (define @t4 () (_ @t3 @t2)) % 0.47/0.66 (define @t5 () (_ @t4 @t1)) % 0.47/0.66 (define @t6 () (@list @t1)) % 0.47/0.66 (define @t7 () (exists @t6 @t5)) % 0.47/0.66 (define @t8 () (@list @t2)) % 0.47/0.66 (define @t9 () (lambda @t8 @t7)) % 0.47/0.66 (define @t10 () (_ tptp.cY_0 @t9)) % 0.47/0.66 (define @t11 () (not (_ tptp.cP_0 (_ (_ tptp.cG_0 @t9) @t10)))) % 0.47/0.66 (define @t12 () (and (_ tptp.cP_0 @t10) @t11)) % 0.47/0.66 (define @t13 () (@var "Xx" $$unsorted)) % 0.47/0.66 (define @t14 () (@var "Xw_20" $$unsorted)) % 0.47/0.66 (define @t15 () (_ @t4 @t14)) % 0.47/0.66 (define @t16 () (@list @t14)) % 0.47/0.66 (define @t17 () (exists @t16 @t15)) % 0.47/0.66 (define @t18 () (lambda @t8 @t17)) % 0.47/0.66 (define @t19 () (_ tptp.cH_0 @t18)) % 0.47/0.66 (define @t20 () (_ tptp.cG_0 @t18)) % 0.47/0.66 (define @t21 () (@list @t13)) % 0.47/0.66 (define @t22 () (lambda @t21 (_ @t20 (_ @t19 @t13)))) % 0.47/0.66 (define @t23 () (exists @t6 (_ (_ @t3 @t22) @t1))) % 0.47/0.66 (define @t24 () (not @t23)) % 0.47/0.66 (define @t25 () (or @t24 @t12)) % 0.47/0.66 (define @t26 () (exists @t6 (_ (_ @t3 @t19) @t1))) % 0.47/0.66 (define @t27 () (exists @t6 (_ (_ @t3 @t20) @t1))) % 0.47/0.66 (define @t28 () (and @t27 @t26 @t25)) % 0.47/0.66 (define @t29 () (@list @t3)) % 0.47/0.66 (define @t30 () (forall @t29 @t28)) % 0.47/0.66 (define @t31 () (@var "BOUND_VARIABLE_7556" (-> (-> $$unsorted $$unsorted) $$unsorted Bool))) % 0.47/0.66 (define @t32 () (_ @t31 @t2 @t1)) % 0.47/0.66 (define @t33 () (not @t32)) % 0.47/0.66 (define @t34 () (forall @t6 @t33)) % 0.47/0.66 (define @t35 () (not @t34)) % 0.47/0.66 (define @t36 () (lambda @t8 @t35)) % 0.47/0.66 (define @t37 () (tptp.cY_0 @t36)) % 0.47/0.66 (define @t38 () (tptp.cG_0 @t36 @t37)) % 0.47/0.66 (define @t39 () (tptp.cP_0 @t38)) % 0.47/0.66 (define @t40 () (tptp.cP_0 @t37)) % 0.47/0.66 (define @t41 () (and @t40 (not @t39))) % 0.47/0.66 (define @t42 () (@var "BOUND_VARIABLE_7596" $$unsorted)) % 0.47/0.66 (define @t43 () (lambda @t8 (not (forall @t16 (not (_ @t31 @t2 @t14)))))) % 0.47/0.66 (define @t44 () (lambda @t21 (tptp.cG_0 @t43 (tptp.cH_0 @t43 @t13)))) % 0.47/0.66 (define @t45 () (not (_ @t31 @t44 @t42))) % 0.47/0.66 (define @t46 () (or @t45 @t41)) % 0.47/0.66 (define @t47 () (@list @t42)) % 0.47/0.66 (define @t48 () (forall @t47 @t46)) % 0.47/0.66 (define @t49 () (@list @t31)) % 0.47/0.66 (define @t50 () (forall @t47 @t45)) % 0.47/0.66 (define @t51 () (or @t50 @t41)) % 0.47/0.66 (define @t52 () (forall @t6 (not (_ @t31 @t44 @t1)))) % 0.47/0.66 (define @t53 () (lambda @t8 (not (forall @t6 (not (_ (_ @t31 @t2) @t1)))))) % 0.47/0.66 (define @t54 () (_ tptp.cY_0 @t53)) % 0.47/0.66 (define @t55 () (_ (_ tptp.cG_0 @t53) @t54)) % 0.47/0.66 (define @t56 () (_ tptp.cG_0 @t36)) % 0.47/0.66 (define @t57 () (_ tptp.cY_0 @t36)) % 0.47/0.66 (define @t58 () (not (_ tptp.cP_0 (_ @t56 @t57)))) % 0.47/0.66 (define @t59 () (and (_ tptp.cP_0 @t57) @t58)) % 0.47/0.66 (define @t60 () (or @t52 @t59)) % 0.47/0.66 (define @t61 () (forall @t49 @t60)) % 0.47/0.66 (define @t62 () (@var "BOUND_VARIABLE_7542" (-> (-> $$unsorted $$unsorted) $$unsorted Bool))) % 0.47/0.66 (define @t63 () (forall (@list @t62) (not (forall @t6 (not (_ @t62 (_ tptp.cH_0 (lambda @t8 (not (forall @t16 (not (_ @t62 @t2 @t14)))))) @t1)))))) % 0.47/0.66 (define @t64 () (@var "BOUND_VARIABLE_7528" (-> (-> $$unsorted $$unsorted) $$unsorted Bool))) % 0.47/0.66 (define @t65 () (forall (@list @t64) (not (forall @t6 (not (_ @t64 (_ tptp.cG_0 (lambda @t8 (not (forall @t16 (not (_ @t64 @t2 @t14)))))) @t1)))))) % 0.47/0.66 (define @t66 () (_ @t3 @t2 @t1)) % 0.47/0.66 (define @t67 () (lambda @t8 (not (forall @t6 (not @t66))))) % 0.47/0.66 (define @t68 () (_ tptp.cY_0 @t67)) % 0.47/0.66 (define @t69 () (_ @t3 @t2 @t14)) % 0.47/0.66 (define @t70 () (not @t69)) % 0.47/0.66 (define @t71 () (forall @t16 @t70)) % 0.47/0.66 (define @t72 () (not @t71)) % 0.47/0.66 (define @t73 () (lambda @t8 @t72)) % 0.47/0.66 (define @t74 () (tptp.cH_0 @t73 @t13)) % 0.47/0.66 (define @t75 () (tptp.cG_0 @t73 @t74)) % 0.47/0.66 (define @t76 () (lambda @t21 @t75)) % 0.47/0.66 (define @t77 () (_ @t3 @t76 @t1)) % 0.47/0.66 (define @t78 () (forall @t6 (not @t77))) % 0.47/0.66 (define @t79 () (or @t78 (and (_ tptp.cP_0 @t68) (not (_ tptp.cP_0 (_ (_ tptp.cG_0 @t67) @t68)))))) % 0.47/0.66 (define @t80 () (forall @t29 @t79)) % 0.47/0.66 (define @t81 () (@list @t3)) % 0.47/0.66 (define @t82 () (_ tptp.cH_0 @t73)) % 0.47/0.66 (define @t83 () (_ @t3 @t82 @t1)) % 0.47/0.66 (define @t84 () (not (forall @t6 (not @t83)))) % 0.47/0.66 (define @t85 () (forall @t29 @t84)) % 0.47/0.66 (define @t86 () (_ tptp.cG_0 @t73)) % 0.47/0.66 (define @t87 () (_ @t3 @t86 @t1)) % 0.47/0.66 (define @t88 () (not (forall @t6 (not @t87)))) % 0.47/0.66 (define @t89 () (forall @t29 @t88)) % 0.47/0.66 (define @t90 () (and @t89 @t85 @t80)) % 0.47/0.66 (define @t91 () (not @t5)) % 0.47/0.66 (define @t92 () (forall @t6 @t91)) % 0.47/0.66 (define @t93 () (not @t92)) % 0.47/0.66 (define @t94 () (not @t15)) % 0.47/0.66 (define @t95 () (forall @t16 @t94)) % 0.47/0.66 (define @t96 () (not @t95)) % 0.47/0.66 (define @t97 () (lambda @t8 @t96)) % 0.47/0.66 (define @t98 () (_ tptp.cH_0 @t97)) % 0.47/0.66 (define @t99 () (_ @t98 @t13)) % 0.47/0.66 (define @t100 () (_ tptp.cG_0 @t97)) % 0.47/0.66 (define @t101 () (_ @t100 @t99)) % 0.47/0.66 (define @t102 () (lambda @t21 @t101)) % 0.47/0.66 (define @t103 () (_ @t82 @t13)) % 0.47/0.66 (define @t104 () (lambda @t21 (_ @t86 @t103))) % 0.47/0.66 (define @t105 () (_ (_ @t3 @t104) @t1)) % 0.47/0.66 (define @t106 () (not @t105)) % 0.47/0.66 (define @t107 () (forall @t6 @t106)) % 0.47/0.66 (define @t108 () (not @t107)) % 0.47/0.66 (define @t109 () (_ (_ @t3 @t82) @t1)) % 0.47/0.66 (define @t110 () (not @t109)) % 0.47/0.66 (define @t111 () (forall @t6 @t110)) % 0.47/0.66 (define @t112 () (not @t111)) % 0.47/0.66 (define @t113 () (_ (_ @t3 @t86) @t1)) % 0.47/0.66 (define @t114 () (not @t113)) % 0.47/0.66 (define @t115 () (forall @t6 @t114)) % 0.47/0.66 (define @t116 () (not @t115)) % 0.47/0.66 (define @t117 () (@var "BOUND_VARIABLE_31410" (-> $$unsorted $$unsorted))) % 0.47/0.66 (define @t118 () (lambda (@list @t117) false)) % 0.47/0.66 (define @t119 () (lambda (@list (@var "BOUND_VARIABLE_14794" (-> $$unsorted $$unsorted)) (@var "BOUND_VARIABLE_14795" $$unsorted)) false)) % 0.47/0.66 (define @t120 () (_ @t119 @t2 @t14)) % 0.47/0.66 (define @t121 () (not @t120)) % 0.47/0.66 (define @t122 () (forall @t16 @t121)) % 0.47/0.66 (define @t123 () (not @t122)) % 0.47/0.66 (define @t124 () (lambda @t8 @t123)) % 0.47/0.66 (define @t125 () (_ @t119 (_ tptp.cG_0 @t124) @t1)) % 0.47/0.66 (define @t126 () (not @t125)) % 0.47/0.66 (define @t127 () (forall @t6 @t126)) % 0.47/0.66 (define @t128 () (not @t127)) % 0.47/0.66 (assume @p1 (not (not @t30))) % 0.47/0.66 (assume @p2 true) % 0.47/0.66 (step @p3 :rule quant-merge-prenex :args ((= (forall @t49 @t48) (forall (@list @t31 @t42) @t46)))) % 0.47/0.66 (step @p4 :rule refl :args (@t41)) % 0.47/0.66 (step @p5 :rule alpha_equiv :args (@t50 (@list @t42) (@list @t1))) % 0.47/0.66 (step @p6 :rule nary_cong :premises (@p5 @p4) :args (@t51)) % 0.47/0.66 (step @p7 :rule quant-miniscope-or :args ((= @t48 @t51))) % 0.47/0.66 (step @p8 :rule trans :premises (@p7 @p6)) % 0.47/0.66 (step @p9 :rule symm :premises (@p8)) % 0.47/0.66 (step @p10 :rule cong :premises (@p9) :args ((forall @t49 (or @t52 @t41)))) % 0.47/0.66 (step @p11 :rule trans :premises (@p10 @p3)) % 0.47/0.66 (step @p12 :rule refl :args ((tptp.cP_0 @t55))) % 0.47/0.66 (step @p13 :rule refl :args ((tptp.cG_0 @t53 @t54))) % 0.47/0.66 (step @p14 :rule refl :args ((tptp.cY_0 @t53))) % 0.47/0.66 (step @p15 :rule refl :args (@t32)) % 0.47/0.66 (step @p16 :rule cong :premises (@p15) :args (@t33)) % 0.47/0.66 (step @p17 :rule cong :premises (@p16) :args (@t34)) % 0.47/0.66 (step @p18 :rule cong :premises (@p17) :args (@t35)) % 0.47/0.66 (step @p19 :rule cong :premises (@p18) :args (@t36)) % 0.47/0.66 (step @p20 :rule cong :premises (@p19) :args (@t37)) % 0.47/0.66 (step @p21 :rule trans :premises (@p20 @p14)) % 0.47/0.66 (step @p22 :rule cong :premises (@p19 @p21) :args (@t38)) % 0.47/0.66 (step @p23 :rule trans :premises (@p22 @p13)) % 0.47/0.66 (step @p24 :rule cong :premises (@p23) :args (@t39)) % 0.47/0.66 (step @p25 :rule trans :premises (@p24 @p12)) % 0.47/0.66 (step @p26 :rule refl :args (tptp.cP_0)) % 0.47/0.66 (step @p27 :rule ho_cong :premises (@p26 @p23)) % 0.47/0.66 (step @p28 :rule cong :premises (@p27 @p25) :args ((= (_ tptp.cP_0 @t38) @t39))) % 0.47/0.66 (step @p29 :rule symm :premises (@p28)) % 0.47/0.66 (step @p30 :rule refl :args ((_ tptp.cP_0 @t55))) % 0.47/0.66 (step @p31 :rule eq_resolve :premises (@p30 @p29)) % 0.47/0.66 (step @p32 :rule refl :args (tptp.cG_0)) % 0.47/0.66 (step @p33 :rule ho_cong :premises (@p32 @p19)) % 0.47/0.66 (step @p34 :rule ho_cong :premises (@p33 @p21)) % 0.47/0.66 (step @p35 :rule cong :premises (@p34 @p23) :args ((= (_ @t56 @t37) @t38))) % 0.47/0.66 (step @p36 :rule symm :premises (@p35)) % 0.47/0.66 (step @p37 :rule refl :args (@t55)) % 0.47/0.66 (step @p38 :rule eq_resolve :premises (@p37 @p36)) % 0.47/0.66 (step @p39 :rule refl :args (tptp.cY_0)) % 0.47/0.66 (step @p40 :rule ho_cong :premises (@p39 @p19)) % 0.47/0.66 (step @p41 :rule cong :premises (@p40 @p21) :args ((= @t57 @t37))) % 0.47/0.66 (step @p42 :rule symm :premises (@p41)) % 0.47/0.66 (step @p43 :rule refl :args (@t54)) % 0.47/0.66 (step @p44 :rule eq_resolve :premises (@p43 @p42)) % 0.47/0.66 (step @p45 :rule refl :args (@t56)) % 0.47/0.66 (step @p46 :rule ho_cong :premises (@p45 @p44)) % 0.47/0.66 (step @p47 :rule trans :premises (@p46 @p38)) % 0.47/0.66 (step @p48 :rule ho_cong :premises (@p26 @p47)) % 0.47/0.66 (step @p49 :rule trans :premises (@p48 @p31)) % 0.47/0.66 (step @p50 :rule cong :premises (@p49) :args (@t58)) % 0.47/0.66 (step @p51 :rule refl :args ((tptp.cP_0 @t54))) % 0.47/0.66 (step @p52 :rule cong :premises (@p21) :args (@t40)) % 0.47/0.66 (step @p53 :rule trans :premises (@p52 @p51)) % 0.47/0.66 (step @p54 :rule ho_cong :premises (@p26 @p21)) % 0.47/0.66 (step @p55 :rule cong :premises (@p54 @p53) :args ((= (_ tptp.cP_0 @t37) @t40))) % 0.47/0.66 (step @p56 :rule symm :premises (@p55)) % 0.47/0.66 (step @p57 :rule refl :args ((_ tptp.cP_0 @t54))) % 0.47/0.66 (step @p58 :rule eq_resolve :premises (@p57 @p56)) % 0.47/0.66 (step @p59 :rule ho_cong :premises (@p26 @p44)) % 0.47/0.66 (step @p60 :rule trans :premises (@p59 @p58)) % 0.47/0.66 (step @p61 :rule nary_cong :premises (@p60 @p50) :args (@t59)) % 0.47/0.66 (step @p62 :rule refl :args (@t52)) % 0.47/0.66 (step @p63 :rule nary_cong :premises (@p62 @p61) :args (@t60)) % 0.47/0.66 (step @p64 :rule cong :premises (@p63) :args (@t61)) % 0.47/0.66 (step @p65 :rule trans :premises (@p64 @p11)) % 0.47/0.66 (step @p66 :rule refl :args (@t63)) % 0.47/0.66 (step @p67 :rule refl :args (@t65)) % 0.47/0.66 (step @p68 :rule nary_cong :premises (@p67 @p66 @p65) :args ((and @t65 @t63 @t61))) % 0.47/0.66 (step @p69 :rule alpha_equiv :args (@t80 @t81 (@list @t31))) % 0.47/0.66 (step @p70 :rule alpha_equiv :args (@t85 @t81 (@list @t62))) % 0.47/0.66 (step @p71 :rule alpha_equiv :args (@t89 @t81 (@list @t64))) % 0.47/0.66 (step @p72 :rule nary_cong :premises (@p71 @p70 @p69) :args (@t90)) % 0.47/0.66 (step @p73 :rule quant-miniscope-and :args ((= (forall @t29 (and @t88 @t84 @t79)) @t90))) % 0.47/0.66 (step @p74 :rule trans :premises (@p73 @p72)) % 0.47/0.66 (step @p75 :rule trans :premises (@p74 @p68)) % 0.47/0.66 (step @p76 :rule refl :args (@t66)) % 0.47/0.66 (step @p77 :rule refl :args (@t5)) % 0.47/0.66 (step @p78 :rule cong :premises (@p77 @p76) :args ((= @t5 @t66))) % 0.47/0.66 (step @p79 :rule symm :premises (@p78)) % 0.47/0.66 (step @p80 :rule eq_resolve :premises (@p77 @p79)) % 0.47/0.66 (step @p81 :rule cong :premises (@p80) :args (@t91)) % 0.47/0.66 (step @p82 :rule cong :premises (@p81) :args (@t92)) % 0.47/0.66 (step @p83 :rule cong :premises (@p82) :args (@t93)) % 0.47/0.66 (step @p84 :rule exists-elim :args ((= @t7 @t93))) % 0.47/0.66 (step @p85 :rule trans :premises (@p84 @p83)) % 0.47/0.66 (step @p86 :rule cong :premises (@p85) :args (@t9)) % 0.47/0.66 (step @p87 :rule refl :args (tptp.cY_0)) % 0.47/0.66 (step @p88 :rule ho_cong :premises (@p87 @p86)) % 0.47/0.66 (step @p89 :rule refl :args (tptp.cG_0)) % 0.47/0.66 (step @p90 :rule ho_cong :premises (@p89 @p86)) % 0.47/0.66 (step @p91 :rule ho_cong :premises (@p90 @p88)) % 0.47/0.66 (step @p92 :rule refl :args (tptp.cP_0)) % 0.47/0.66 (step @p93 :rule ho_cong :premises (@p92 @p91)) % 0.47/0.66 (step @p94 :rule cong :premises (@p93) :args (@t11)) % 0.47/0.66 (step @p95 :rule ho_cong :premises (@p92 @p88)) % 0.47/0.66 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t12)) % 0.47/0.66 (step @p97 :rule bool-double-not-elim :args (@t78)) % 0.47/0.66 (step @p98 :rule refl :args ((_ @t3 @t102 @t1))) % 0.47/0.66 (step @p99 :rule refl :args (@t1)) % 0.47/0.66 (step @p100 :rule refl :args ((tptp.cG_0 @t97 @t99))) % 0.47/0.66 (step @p101 :rule refl :args ((tptp.cH_0 @t97 @t13))) % 0.47/0.66 (step @p102 :rule refl :args (@t13)) % 0.47/0.66 (step @p103 :rule refl :args (@t69)) % 0.47/0.66 (step @p104 :rule cong :premises (@p103) :args (@t70)) % 0.47/0.66 (step @p105 :rule cong :premises (@p104) :args (@t71)) % 0.47/0.66 (step @p106 :rule cong :premises (@p105) :args (@t72)) % 0.47/0.66 (step @p107 :rule cong :premises (@p106) :args (@t73)) % 0.47/0.66 (step @p108 :rule cong :premises (@p107 @p102) :args (@t74)) % 0.47/0.66 (step @p109 :rule trans :premises (@p108 @p101)) % 0.47/0.66 (step @p110 :rule cong :premises (@p107 @p109) :args (@t75)) % 0.47/0.66 (step @p111 :rule trans :premises (@p110 @p100)) % 0.47/0.66 (step @p112 :rule cong :premises (@p111) :args (@t76)) % 0.47/0.66 (step @p113 :rule cong :premises (@p112 @p99) :args (@t77)) % 0.47/0.66 (step @p114 :rule trans :premises (@p113 @p98)) % 0.47/0.66 (step @p115 :rule refl :args (@t3)) % 0.47/0.66 (step @p116 :rule ho_cong :premises (@p115 @p112)) % 0.47/0.66 (step @p117 :rule ho_cong :premises (@p116 @p99)) % 0.47/0.66 (step @p118 :rule cong :premises (@p117 @p114) :args ((= (_ (_ @t3 @t76) @t1) @t77))) % 0.47/0.66 (step @p119 :rule symm :premises (@p118)) % 0.47/0.66 (step @p120 :rule refl :args ((_ (_ @t3 @t102) @t1))) % 0.47/0.66 (step @p121 :rule eq_resolve :premises (@p120 @p119)) % 0.47/0.66 (step @p122 :rule ho_cong :premises (@p32 @p107)) % 0.47/0.66 (step @p123 :rule ho_cong :premises (@p122 @p109)) % 0.47/0.66 (step @p124 :rule cong :premises (@p123 @p111) :args ((= (_ @t86 @t74) @t75))) % 0.47/0.66 (step @p125 :rule symm :premises (@p124)) % 0.47/0.66 (step @p126 :rule refl :args (@t101)) % 0.47/0.66 (step @p127 :rule eq_resolve :premises (@p126 @p125)) % 0.47/0.66 (step @p128 :rule refl :args (tptp.cH_0)) % 0.47/0.66 (step @p129 :rule ho_cong :premises (@p128 @p107)) % 0.47/0.66 (step @p130 :rule ho_cong :premises (@p129 @p102)) % 0.47/0.66 (step @p131 :rule cong :premises (@p130 @p109) :args ((= @t103 @t74))) % 0.47/0.66 (step @p132 :rule symm :premises (@p131)) % 0.47/0.66 (step @p133 :rule refl :args (@t99)) % 0.47/0.66 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 0.47/0.66 (step @p135 :rule refl :args (@t86)) % 0.47/0.66 (step @p136 :rule ho_cong :premises (@p135 @p134)) % 0.47/0.66 (step @p137 :rule trans :premises (@p136 @p127)) % 0.47/0.66 (step @p138 :rule cong :premises (@p137) :args (@t104)) % 0.47/0.66 (step @p139 :rule ho_cong :premises (@p115 @p138)) % 0.47/0.66 (step @p140 :rule ho_cong :premises (@p139 @p99)) % 0.47/0.66 (step @p141 :rule trans :premises (@p140 @p121)) % 0.47/0.66 (step @p142 :rule cong :premises (@p141) :args (@t106)) % 0.47/0.66 (step @p143 :rule cong :premises (@p142) :args (@t107)) % 0.47/0.66 (step @p144 :rule cong :premises (@p143) :args (@t108)) % 0.47/0.66 (step @p145 :rule exists-elim :args ((= (exists @t6 @t105) @t108))) % 0.47/0.66 (step @p146 :rule trans :premises (@p145 @p144)) % 0.47/0.66 (step @p147 :rule refl :args (@t1)) % 0.47/0.66 (step @p148 :rule refl :args (@t13)) % 0.47/0.66 (step @p149 :rule refl :args (@t15)) % 0.47/0.66 (step @p150 :rule cong :premises (@p149 @p103) :args ((= @t15 @t69))) % 0.47/0.66 (step @p151 :rule symm :premises (@p150)) % 0.47/0.66 (step @p152 :rule eq_resolve :premises (@p149 @p151)) % 0.47/0.66 (step @p153 :rule cong :premises (@p152) :args (@t94)) % 0.47/0.66 (step @p154 :rule cong :premises (@p153) :args (@t95)) % 0.47/0.66 (step @p155 :rule cong :premises (@p154) :args (@t96)) % 0.47/0.66 (step @p156 :rule exists-elim :args ((= @t17 @t96))) % 0.47/0.66 (step @p157 :rule trans :premises (@p156 @p155)) % 0.47/0.66 (step @p158 :rule cong :premises (@p157) :args (@t18)) % 0.47/0.66 (step @p159 :rule refl :args (tptp.cH_0)) % 0.47/0.66 (step @p160 :rule ho_cong :premises (@p159 @p158)) % 0.47/0.66 (step @p161 :rule ho_cong :premises (@p160 @p148)) % 0.47/0.66 (step @p162 :rule ho_cong :premises (@p89 @p158)) % 0.47/0.66 (step @p163 :rule ho_cong :premises (@p162 @p161)) % 0.47/0.66 (step @p164 :rule cong :premises (@p163) :args (@t22)) % 0.47/0.66 (step @p165 :rule refl :args (@t3)) % 0.47/0.66 (step @p166 :rule ho_cong :premises (@p165 @p164)) % 0.47/0.66 (step @p167 :rule ho_cong :premises (@p166 @p147)) % 0.47/0.66 (step @p168 :rule cong :premises (@p167) :args (@t23)) % 0.47/0.66 (step @p169 :rule trans :premises (@p168 @p146)) % 0.47/0.66 (step @p170 :rule cong :premises (@p169) :args (@t24)) % 0.47/0.66 (step @p171 :rule trans :premises (@p170 @p97)) % 0.47/0.66 (step @p172 :rule nary_cong :premises (@p171 @p96) :args (@t25)) % 0.47/0.66 (step @p173 :rule refl :args ((_ @t3 @t98 @t1))) % 0.47/0.66 (step @p174 :rule cong :premises (@p129 @p99) :args (@t83)) % 0.47/0.66 (step @p175 :rule trans :premises (@p174 @p173)) % 0.47/0.66 (step @p176 :rule ho_cong :premises (@p115 @p129)) % 0.47/0.66 (step @p177 :rule ho_cong :premises (@p176 @p99)) % 0.47/0.66 (step @p178 :rule cong :premises (@p177 @p175) :args ((= @t109 @t83))) % 0.47/0.66 (step @p179 :rule symm :premises (@p178)) % 0.47/0.66 (step @p180 :rule refl :args ((_ (_ @t3 @t98) @t1))) % 0.47/0.66 (step @p181 :rule eq_resolve :premises (@p180 @p179)) % 0.47/0.66 (step @p182 :rule cong :premises (@p181) :args (@t110)) % 0.47/0.66 (step @p183 :rule cong :premises (@p182) :args (@t111)) % 0.47/0.66 (step @p184 :rule cong :premises (@p183) :args (@t112)) % 0.47/0.66 (step @p185 :rule exists-elim :args ((= (exists @t6 @t109) @t112))) % 0.47/0.66 (step @p186 :rule trans :premises (@p185 @p184)) % 0.47/0.66 (step @p187 :rule ho_cong :premises (@p165 @p160)) % 0.47/0.66 (step @p188 :rule ho_cong :premises (@p187 @p147)) % 0.47/0.66 (step @p189 :rule cong :premises (@p188) :args (@t26)) % 0.47/0.66 (step @p190 :rule trans :premises (@p189 @p186)) % 0.47/0.66 (step @p191 :rule refl :args ((_ @t3 @t100 @t1))) % 0.47/0.66 (step @p192 :rule cong :premises (@p122 @p99) :args (@t87)) % 0.47/0.66 (step @p193 :rule trans :premises (@p192 @p191)) % 0.47/0.66 (step @p194 :rule ho_cong :premises (@p115 @p122)) % 0.47/0.66 (step @p195 :rule ho_cong :premises (@p194 @p99)) % 0.47/0.66 (step @p196 :rule cong :premises (@p195 @p193) :args ((= @t113 @t87))) % 0.47/0.66 (step @p197 :rule symm :premises (@p196)) % 0.47/0.66 (step @p198 :rule refl :args ((_ (_ @t3 @t100) @t1))) % 0.47/0.66 (step @p199 :rule eq_resolve :premises (@p198 @p197)) % 0.47/0.66 (step @p200 :rule cong :premises (@p199) :args (@t114)) % 0.47/0.66 (step @p201 :rule cong :premises (@p200) :args (@t115)) % 0.47/0.66 (step @p202 :rule cong :premises (@p201) :args (@t116)) % 0.47/0.66 (step @p203 :rule exists-elim :args ((= (exists @t6 @t113) @t116))) % 0.47/0.66 (step @p204 :rule trans :premises (@p203 @p202)) % 0.47/0.66 (step @p205 :rule ho_cong :premises (@p165 @p162)) % 0.47/0.66 (step @p206 :rule ho_cong :premises (@p205 @p147)) % 0.47/0.66 (step @p207 :rule cong :premises (@p206) :args (@t27)) % 0.47/0.66 (step @p208 :rule trans :premises (@p207 @p204)) % 0.47/0.66 (step @p209 :rule nary_cong :premises (@p208 @p190 @p172) :args (@t28)) % 0.47/0.66 (step @p210 :rule cong :premises (@p209) :args (@t30)) % 0.47/0.66 (step @p211 :rule trans :premises (@p210 @p75)) % 0.47/0.66 (step @p212 :rule bool-double-not-elim :args (@t30)) % 0.47/0.66 (step @p213 :rule trans :premises (@p212 @p211)) % 0.47/0.66 (step @p214 :rule eq_resolve :premises (@p1 @p213)) % 0.47/0.66 (step @p215 :rule and_elim :premises (@p214) :args (0)) % 0.47/0.66 (step @p216 :rule bool-impl-false1 :args (@t65)) % 0.47/0.66 (step @p217 :rule evaluate :args ((not true))) % 0.47/0.66 (step @p218 :rule quant-unused-vars :args ((= (forall @t6 true) true))) % 0.47/0.66 (step @p219 :rule evaluate :args ((not false))) % 0.47/0.66 (step @p220 :rule beta-reduce :args ((= (_ @t119 (_ tptp.cG_0 @t118) @t1) false))) % 0.47/0.66 (step @p221 :rule refl :args (@t118)) % 0.47/0.66 (step @p222 :rule symm :premises (@p221)) % 0.47/0.66 (step @p223 :rule alpha_equiv :args ((lambda @t8 false) (@list @t2) (@list @t117))) % 0.47/0.66 (step @p224 :rule trans :premises (@p223 @p222)) % 0.47/0.66 (step @p225 :rule quant-unused-vars :args ((= (forall @t16 true) true))) % 0.47/0.66 (step @p226 :rule beta-reduce :args ((= @t120 false))) % 0.47/0.66 (step @p227 :rule cong :premises (@p226) :args (@t121)) % 0.47/0.66 (step @p228 :rule trans :premises (@p227 @p219)) % 0.47/0.66 (step @p229 :rule cong :premises (@p228) :args (@t122)) % 0.47/0.66 (step @p230 :rule trans :premises (@p229 @p225)) % 0.47/0.66 (step @p231 :rule cong :premises (@p230) :args (@t123)) % 0.47/0.66 (step @p232 :rule trans :premises (@p231 @p217)) % 0.47/0.66 (step @p233 :rule cong :premises (@p232) :args (@t124)) % 0.47/0.66 (step @p234 :rule trans :premises (@p233 @p224)) % 0.47/0.66 (step @p235 :rule ho_cong :premises (@p89 @p234)) % 0.47/0.66 (step @p236 :rule cong :premises (@p235 @p147) :args (@t125)) % 0.47/0.66 (step @p237 :rule trans :premises (@p236 @p220)) % 0.47/0.66 (step @p238 :rule cong :premises (@p237) :args (@t126)) % 0.47/0.66 (step @p239 :rule trans :premises (@p238 @p219)) % 0.47/0.66 (step @p240 :rule cong :premises (@p239) :args (@t127)) % 0.47/0.66 (step @p241 :rule trans :premises (@p240 @p218)) % 0.47/0.66 (step @p242 :rule cong :premises (@p241) :args (@t128)) % 0.47/0.66 (step @p243 :rule trans :premises (@p242 @p217)) % 0.47/0.66 (step @p244 :rule cong :premises (@p67 @p243) :args ((=> @t65 @t128))) % 0.47/0.66 (step @p245 :rule trans :premises (@p244 @p216)) % 0.47/0.66 (assume-push @p252 @t65) % 0.47/0.66 (step @p247 :rule instantiate :premises (@p215) :args ((@list @t119))) % 0.47/0.66 (step-pop @p253 :rule scope :premises (@p247)) % 0.47/0.66 (step @p248 :rule process_scope :premises (@p253) :args (@t128)) % 0.47/0.66 (step @p250 :rule eq_resolve :premises (@p248 @p245)) % 0.47/0.66 (step @p251 false :rule chain_m_resolution :premises (@p250 @p215) :args (false (@list false) (@list @t65))) % 0.47/0.66 ) % 0.47/0.66 % SZS output end Proof % 0.47/0.66 % cvc5 exiting %------------------------------------------------------------------------------